On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)

Let ∆ denote the discriminant of the generic binary d-ic. We show that for d ≥ 3, the Jacobian ideal of ∆ is perfect of height 2. Moreover we describe its SL2-equivariant minimal resolution and the associated differential equations satisfied by ∆. A similar result is proved for the resultant of two...

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Detalles Bibliográficos
Autores: D'Andrea, Carlos, 1973-, Chipalkatti, Jaydeep
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/16913
Acceso en línea:https://hdl.handle.net/2445/16913
Access Level:acceso abierto
Palabra clave:Geometria algebraica
Algebraic geometry
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spelling On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)D'Andrea, Carlos, 1973-Chipalkatti, JaydeepGeometria algebraicaAlgebraic geometryLet ∆ denote the discriminant of the generic binary d-ic. We show that for d ≥ 3, the Jacobian ideal of ∆ is perfect of height 2. Moreover we describe its SL2-equivariant minimal resolution and the associated differential equations satisfied by ∆. A similar result is proved for the resultant of two forms of orders d, e whenever d ≥ e − 1. If Φn denotes the locus of binary forms with total root multiplicity ≥ d − n, then we show that the ideal of Φn is also perfect, and we construct a covariant which characterizes this locus. We also explain the role of the Morley form in the determinantal formula for the resultant. This relies upon a calculation which is done in the appendix by A. Abdesselam.Universitat de Barcelona201120112007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion26 p.application/pdfhttps://hdl.handle.net/2445/16913Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: http://www.collectanea.ub.edu/index.php/Collectanea/article/view/4107/5023Collectanea Mathematica, 2007, vol. 58, num. 2, p. 155-180(c) Universitat de Barcelona, 2007info:eu-repo/semantics/openAccessoai:recercat.cat:2445/169132026-05-29T05:05:01Z
dc.title.none.fl_str_mv On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
title On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
spellingShingle On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
D'Andrea, Carlos, 1973-
Geometria algebraica
Algebraic geometry
title_short On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
title_full On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
title_fullStr On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
title_full_unstemmed On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
title_sort On the Jacobian ideal of the binary discriminant (with an appendix by Abdelmalek Abdesselam)
dc.creator.none.fl_str_mv D'Andrea, Carlos, 1973-
Chipalkatti, Jaydeep
author D'Andrea, Carlos, 1973-
author_facet D'Andrea, Carlos, 1973-
Chipalkatti, Jaydeep
author_role author
author2 Chipalkatti, Jaydeep
author2_role author
dc.subject.none.fl_str_mv Geometria algebraica
Algebraic geometry
topic Geometria algebraica
Algebraic geometry
description Let ∆ denote the discriminant of the generic binary d-ic. We show that for d ≥ 3, the Jacobian ideal of ∆ is perfect of height 2. Moreover we describe its SL2-equivariant minimal resolution and the associated differential equations satisfied by ∆. A similar result is proved for the resultant of two forms of orders d, e whenever d ≥ e − 1. If Φn denotes the locus of binary forms with total root multiplicity ≥ d − n, then we show that the ideal of Φn is also perfect, and we construct a covariant which characterizes this locus. We also explain the role of the Morley form in the determinantal formula for the resultant. This relies upon a calculation which is done in the appendix by A. Abdesselam.
publishDate 2007
dc.date.none.fl_str_mv 2007
2011
2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/16913
url https://hdl.handle.net/2445/16913
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: http://www.collectanea.ub.edu/index.php/Collectanea/article/view/4107/5023
Collectanea Mathematica, 2007, vol. 58, num. 2, p. 155-180
dc.rights.none.fl_str_mv (c) Universitat de Barcelona, 2007
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Universitat de Barcelona, 2007
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 26 p.
application/pdf
dc.publisher.none.fl_str_mv Universitat de Barcelona
publisher.none.fl_str_mv Universitat de Barcelona
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
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